g > r is a sustainability condition, not a welfare improvement condition

g > r has made a reappearance in the debt debates. Initially everybody ignored it becaue we were focusing on what was really fundamental about debt, but I think everybody pretty much accepts the Samuelsonian point as a practical matter. If your growth rate is greater than the interest rate, you're in the clear on the debt. If you complicate it a little more you can pull out a level of deficits that you can run each year and still maintain a stable debt level (relative to GDP). But g > r is good enough short hand for all these sustainable cases.

But I want to take a step back because g > r doesn't exactly smooth over all the problems with the debt debate we've been holding.

g > r means the economy can sustain a debt burden. It does not mean that that debt burden won't cost future generations (it doesn't add any more future value costs that taxation in the current period for the same expenditure wouldn't add, of course). To make the debt expenditure itself benefit everybody its not enough that g is greater than r. The rate of return on the expenditure has to be greater than r.

Think about it this way - let's say the economy was growing at g for reasons completely unrelated to the debt expenditure. If g > r then you can pay that debt, right? But if g isn't boosted by the debt expenditure then the public is still worse off than it would have been. Why not just forget the debt expenditure and just enjoy g without the debt service taken out of it?

So it's important to keep in mind that g > r is a sustainability condition, not a welfare improvement condition. To improve welfare, the expenditure has to be worth it, either because we care that much about the consumption or transfer that its supporting or because the expenditure is making an investmnet that will pay off down the road.

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I would point out one thing: it is a public service to explain g > r to people. If you tell the man on the street that we can run deficits every year until the end of time without increasing the burden of the debt, they typically don't respond well to that.